Abstract
The linear differential equation of the Fuchsian class with six regular singular points, which corresponds to the problem of conformal mapping of circular hexagons in polar networks with two sections, is considered. It is shown that when fixing the parameter, which characterizes the deviation of the radii of the circles constituting the opposite sides of the polygon, on which the sections can appear, the configuration and mutual arrangement of the latter depend substantially not only and not even mainly on the known properties of θ functions, based on which the partial solutions of the equation under consideration are constructed, but mainly on the ranges of varying the unknown constants of the conformal mapping, which enter the expressions for imaging functions. The results of numerical calculations are presented.
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